On two conjectures about set-graceful graphs (Q914706)

The paper deals with set-graceful graphs. \textit{B. D. Acharya} introduced the notion of set-graceful graphs in [M.R.I. Lect. Notes Appl. Math. 2, Allahabad 1983]. A graph \(G=(V,E)\) is set-graceful iff there exist a non- empty set X and an injection f: \(V\to P(X)\) (where P(X) denotes the power set of X) such that \(f^{\Delta}(E)=P(X)-\{\phi \},\) where \(f^{\Delta}\) is the well-known symmetric difference. The two authors succeed in proving the Acharya conjecture that every cycle of length \(2^ m-1\), \(m\geq 2\), is set-graceful, and conclude by disproving a second Acharaya conjecture referring certain complete graphs.